Nucleation of creases and folds in hyperelastic solids is not a local bifurcation

We consider creases and folds in compressed hyperelastic solids from the point of view bifurcation theory. They refer to highly localized surface deformations that occur at compressive loads significantly below value well-known Biot instability. Much work literature attempts make case this phenomenon corresponds a “ local ” distinct A is path equilibrium solutions emanating (bifurcation) on trivial solution branch exists all sufficiently small neighborhoods point. The inference usually made by first introducing imperfection; curve then obtained seemingly close perfect diagram. However, imperfection theory valid only some neighborhood Thus, absence an connecting these one, there no justification for concluding creasing folding are bifurcations system. In work, we directly address nucleation perfect, imperfection-free case. demonstrate instabilities functionally graded bilayer elastic halfspaces, corresponding homogeneous state, necessarily smooth oscillatory; creases/folds eventually do develop along global bifurcating branches, albeit far solution, as evidenced diagrams. addition, find their stable realization occurs load levels well initial Moreover, obtain such results halfspace , switching continuation parameter macroscopic lateral strain film-to-substrate shear modulus ratio. When ratio reaches unity, desired deformation avoiding need analysis near degenerate state